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Table 1 Parameter values

From: Origin of the blood hyperserotonemia of autism

Parameter

Value

Units

Source

Note

  

(plt = platelet)

  

MW (5-HT)

176.22

g mol-1

 

1

D

6.00 · 10-8

m2 min-1

[48]

2

d b

6.00

m3 min-1

d b = DS/w

3

d g

5.82 · 103

min-1

d g = d b g

4

G 0

1.00 · 10-6

mol m-3

Table 1 of [32]

5

k g

4.00

min-1

Fig. 4A of [35]

6

k p

2.12 · 10-15

m3 min-1 plt-1

[18]

7

R 0

1.65 · 10-5

mol m-3 min-1

[14]

8

P 0

3.58 · 10-18

mol plt-1

[7]

9

S

1.00 · 102

m2

Table 8.3 of [48]

10

Q tot

5.60 · 10-3

m3 min-1

[14]

11

t 1/2

7.20 · 103

min

[28, 29]

12

w

1.00 · 10-6

m

Table 8.2 of [48]

13

z g

0.27

 

Fig. 1 of [14]

14

z ng

0.73

 

z ng = 1 - z g

15

α

≥ 0

min-1

See note

16

β

≥ 0

plt m-3 min-1

See note

17

θ h

0.25

 

[13]

18

θ p

0.08

 

[13]

19

θ v

0.50

 

[13]

20

ρ

9.70 · 104

m-1

ρ = S g

21

σ

0.56

 

See note

22

τ

1.04 · 104

min

τ = 1.44t1/2

23

Ω b

5.40 · 10-3

m3

Table 8.3 of [48]

24

Ω g

1.03 · 10-3

m3

[49]

25

  1. 1. The molecular weight of 5-HT (C10H12N2O).
  2. 2. The coefficient of 5-HT diffusion across the gut capillary wall. In liquids, the diffusion coefficient is on the order of 10-5 cm2/s [48].
  3. 3. The rate constant of 5-HT influx into the blood due to 5-HT diffusion from the gut.
  4. 4. The rate constant of 5-HT loss in the gut due to 5-HT diffusion into the blood.
  5. 5. The homeostatic set point of the extracellular 5-HT concentration in the gut mucosa (irrelevant if α = 0). The concentration of extracellular 5-HT in the gut wall is unknown. We used an estimate based on extracellular 5-HT levels in the rat raphe nuclei [32]. Both the raphe nuclei and the gut mucosa synthesize 5-HT and express some of the same 5-HT receptors, such as the 5-HT1A receptor [32, 39].
  6. 6. The 5-HT uptake rate constant of the gut mucosa is unknown. We used an estimate based on measurements of 5-HT uptake in the normal (SERT +/+) rat brain [35]. The value of V max was assumed to be 4 pmol/min per milligram of protein [35], the protein content in the brain was assumed to be 10% (w/w) [50], and the specific weight of fresh brain tissue was 1 g/mL [51]. This yielded V max = 4 · 10-4 mol/min per cubic meter of fresh tissue. The value of K m was assumed to be 100 nmol/L [35]. Since K m is much larger than the extracellular 5-HT concentration [32], k g was calculated as V max /K m . (As this article was being prepared for publication, Gill et al. [52] published a detailed report on the expression and kinetics of the human gut SERT.)
  7. 7. The 5-HT uptake rate constant of one platelet. The V max and and K m values were obtained by weighting the medians of each of the three groups of [18] by the number of subjects in the study. Since K m is much larger than the concentration of free 5-HT in the blood plasma [14], k p was calculated as V max /K m .
  8. 8. The gut 5-HT release rate that is independent of both the extracellular 5-HT concentration in the gut wall and the platelet 5-HT concentration. The gut 5-HT production estimate of 3000 ng/min was used [14]. In order to obtain the 5-HT release rate per unit volume of the gut wall (R0), this estimate was divided by Ω g and further assumed to be independent of Ω g .
  9. 9. The homeostatic set point for the platelet 5-HT concentration (irrelevant if β = 0).
  10. 10. The total surface area of blood capillaries in the gut was assumed to be on the order of 108 mm2, since the total surface of the body capillaries has been estimated to be 2.98 · 108 mm2 [48].
  11. 11. The total cardiac output.
  12. 12. The half-life of blood platelets.
  13. 13. The wall thickness of blood capillaries in the gut.
  14. 14. The proportion of the total cardiac output routed to the gut and/or the liver (Fig. 1).
  15. 15. The proportion of the total cardiac output not routed to the gut and/or the liver (Fig. 1).
  16. 16. The gain of the regulation of the gut 5-HT release rate that is controlled by extracellular 5-HT concentration in the gut wall.
  17. 17. The gain of the regulation of the gut 5-HT release rate that is controlled by platelet 5-HT concentration.
  18. 18. One minus the proportion of free 5-HT in the blood plasma that is removed by the liver in one cycle of blood circulation. Based on an estimate obtained in the dog [13].
  19. 19. One minus the proportion of free 5-HT in the blood plasma that is removed by the lungs in one cycle of blood circulation. Based on an estimate obtained in the dog [13].
  20. 20. One minus the proportion of free 5-HT in the blood plasma that is removed in the "non-gut" (NG) system (Fig. 1) in one cycle of blood circulation. Based on estimates obtained in the dog [13].
  21. 21. The surface area of blood capillaries per unit volume of the gut mucosa.
  22. 22. The proportion of blood volume not occupied by cells. It is approximated well by 1 - Ht, where Ht = 0.44 is the hematocrit.
  23. 23. The time constant of platelet removal from the blood circulation.
  24. 24. The total volume of the circulating blood.
  25. 25. The total volume of the gut wall. Since EC cells are distributed from the stomach through the colon [10], the gut was assumed to be a cylinder with a length of 8 m and a diameter of 4 cm. The gut mucosa contains both the main source of peripheral 5-HT (the EC cells) and a dense meshwork of blood capillaries [53]. Therefore, the effective width of the gut wall was considered to be equal to the average length of the villi of the mucosa, or around 1 mm [49].